When you click the Publish button and the Check for Errors button, SharePoint Designer 2013 crashes and restarts. However, this occurs again even when restarted.
Solution I applied:
I re-installed SharePoint Designer 2013 on my developer workstation. Repairing it through Programs and Features does not solve the issue.
I have encountered this issue several times now and re-installing it indeed solves the issue.
Unknown for now.